Flaps

An examination of all of the airfoil data presented in Reference 3.1 discloses that the greatest value of Cimax one can expect at a high Reynolds number from an ordinary airfoil is around 1.8. This maximum value is achieved by the NACA 23012 airfoil. Another 12% thick airfoil, the 2412, delivers the second highest value, 1.7.

In order to achieve higher Cimax values for takeoff and landing without unduly penalizing an airplane’s cruising performance, one resorts to the use of mechanical devices to alter temporarily the geometry of the airfoil. These devices, known as flaps, exist in many different configurations, the most common of which are illustrated in Figure 3.24. In addition to the purely mechanical flaps, this figure depicts flaps that can be formed by sheets of air exiting at the trailing edge. These “jet flaps” can produce C(max values in excess of those from mechanical flaps, provided sufficient energy and momentum are contained in the jet. Frequently one uses the terms “powered” and “unpowered” to distinguish between jet and mechanical flaps.

The effect of a mechanical flap can be seen by referring once again to Figure 3.6. Deflecting the flap, in this case a split flap, is seen to shift the lift curve upward without changing the slope. This is as one might expect from Equation 3.26, since deflecting the flap is comparable to adding camber to the airfoil.

Some flap configurations appear to be significantly better than others simply because, when deflected, they extend the original chord on which the lift coefficient is based. One can determine if the flap is extensible, such as the Fowler or Zap flaps in Figure 3.24, by noting whether or not the slope of the lift curve is increased with the flap deflected. Consider a flap that, when deflected, extends the original chord by the fraction x. The physical lift curve would have a slope given by

~ = ^PV2( + x)cCla (3.43)

since (l + x)c is the actual chord. Qa does not depend significantly on thickness or camber; hence, the lift curve slope of the flapped airfoil based on the unflapped chord, c, would be

Cia (flapped) = (1 + jc)Q_ (unflapped)

Now the maximum lift, expressed in terms of the extended chord and C;maXe

■Lmax = 2 РУ2(1 + *)cCLxe

based on the original chord becomes

C, =(1 + x)C, ~~

•max v ‘ ‘max.

Figure 3.25 Performance of plain flaps, (a) Variation of maximum section lift coefficient with flap deflection for several airfoil sections equipped with plain flaps, (b) Variation of optimum increment of maximum section lift coefficient with flap chord ratio for several airfoil sections equipped with plain flaps, (c) Effect of gap seal on maximum lift coefficient of a rectangular Clark-Y wing equipped with a full-span 0.20c plain flap. A = 6, Я = 0.6 x Ю4.

Figure 3.26 Variation of maximum section lift coefficient with flap deflection for three NACA 230-series airfoils equipped with split flaps of various sizes. R = 3.5 x 10®. (a) NACA 23012 airfoil section, (b) NACA 23021 airfoil section, (c) NACA 23030 airfoil section.

Figures 3.25 to 3.30 and Tables 3.1 and 3.2 present section data on plain, split, and slotted flaps as reported in Reference 3.15. With these data one should be able to estimate reasonably accurately the characteristics of an airfoil section equipped with flaps.

A study of this data suggests the following:

Plain Flaps

1. The optimum flap chord ratio is approximately 0.25.

2. The optimum flap angle is approximately 60°.

3. Leakage through gap at flap nose can decrease C(max by approximately 0.4.

4. The maximum achievable increment in C|max is approximately 0.9.

Split Flaps

1. The optimum flap chord ratio is approximately 0.3 for 12% thick airfoils, increasing to 0.4 or higher for thicker airfoils.

2. The optimum flap angle is approximately 70°.

3. The maximum achievable increment in С/тал is approximately 0.9.

4. CL, increases nearly linearly with log R for 0.7 x 106 < R < 6 x 106.

5. The optimum thickness ratio is approximately 18%.

0.5 0.7 1.0 2.0 3.0 4.0 5.0 0.5 0.7 1.0 2.0 3.0 4.0 5.0 X106 X 106 Reynolds number, R Reynolds number, R Figure 3.27 Variation of maximum section lift coefficient with Reynolds number for several NACA airfoil sections with and without 0.20c split flaps deflected 60°. (a) Smooth airfoil, (b) Airfoil with leading edge roughness.

Slotted Flaps

1. The optimum flap chord ratio is approximately 0.3.

2. The optimum flap angle is approximately 40° for single slots and 70° for double-slotted flaps.

3. The optimum thickness ratio is approximately 16%.

4- Cw is sensitive to flap (and vane) position.

5. The maximum achievable increment in C(max is approximately 1.5 for single slots and 1.9 for double slotted flaps.

Figure 3.28 Contours of flap and vane positions for maximum section lift coefficient for several airfoil sections equipped with double-slotted flaps, (a) NACA 23012 airfoil section; 5, = 60°. (b) NACA 23021 airfoil section; Sf = 60°. (c) NACA 611-212 airfoil section.

Airfoil thickness ratio, — c Figure 3.29 Maximum section lift coefficients for several NACA airfoil sections with double-slotted and split flaps.

Referring to Equation 3.44 and Figure 3.30, it is obvious that some of the superior performance of the double-slotted flap results from the extension of the chord. From the figure, C(a (flapped) is equal to 0.12 C(/deg as compared to the expected unflapped value of approximately 0.1. Hence, based on the actual chord, the increment in for the double-slotted flap is only 1.6. However, this is still almost twice that afforded by plain or split flaps and points to the beneficial effect of the slot in delaying separation.

Figure 3.31 (taken from Ref. 3.15) presents pitching moment data for flapped airfoil sections. The lift and moment are taken to act at the aerody­namic center of the airfoil, located approximately 25% of the chord back from the leading edge. The moment is positive if it tends to increase the angle of attack.

From Figure 3.31, the lowering of a flap results in an incremental pitching moment. In order to trim the airplane a download must /be produced on the horizontal tail. The wing must now support this download in addition to the aircraft’s weight. Hence the effective increment in lift due to the flap is less than that which the wing-flap combination produces alone. This correction can typically reduce by 0.1 to 0.3.

Section lift coefficient,

Figure 3.30 Section lift characteristics of an NACA 63, 4-421 (approximately) airfoil equipped with a double-slotted flap and several slot-entry-skirt extensions, (a) No skirt extension; R = 2.4x 104. (b) Partial skirt extension; R = 2.4x 10®. (c) Partial skirt extension; Я = 6.0 x 10®. (d) Full skirt extension; Я = 2.4 x 10®.

b	A	2.79	50	0.015	0.025	Yes	3.5
a	A	2.88	50	0.015	0.045	Yes	3.5
b	В	2.59	60	0.025	0.040	Yes	3.5
a	В	2.68	60	-0.005	0.040	Yes	3.5
b	В	2.82	50	0.025	0.060	Yes	3.5
a	В	2.90	50	0.025	0.060	Yes	3.5
b	В	3.00	35	0.018	0.045	No	6.0
a	А	3.21	’40	0	0.027	Yes	9.0
c	А	2.47	45	0.009	0.010	Yes	6.0
c	А	2.48	41.3	0.014	0.009	Yes	6.0
c	А	2.45	35	0.004	0.020	Yes	6.0
c	А	2.69	35	-0.020	0.032	Yes	9.0
c	А	2.63	40	0.019	0.046	No	9.0
c	А	2.80	40	0.019	0.038	No	9.0
a	В	2.83	30	0.025	0.046	Yes	9.95
c	В	2.70	55	0	0.028	No	6.0
a	А	2.69	45	0.017	0.038	No	6.0
c	А	2.92	37	0	0.016	No	6.0
a	А	2.89	40	0.023	0.040	Yes	5.1
c	А	2.88	45	0.011	0.031	Yes	5.1
		2.68	32.5			No	6.0

Typical single—slotted flap configuration, dimensions are given in fractions of airfoil chord.)

oment coefficient, (a)

M Figure 3.31 (Continued)

In a high-wing airplane, lowering the flaps can cause the nose to pitch up. This is due to the moment produced about the center of gravity from the increase in wing drag because of the flaps. Based on the wing area, the increment in wing drag coefficient, Д Co, due to the flaps is given ap­proximately by,

ДCD = 1.7(cflc)l3S(SflS) sin2S/ (plain and split) (3.45)

= 0.9(cflc)’ x(SfIS) sin2Sf (slotted) (3.46)

If the wing is located a height of h above the center of gravity, a balancing upload is required on the tail. The effect of trim on for a complete airplane will be discussed in more detail later.

Flap Effectiveness in the Linear Range

Frequently one needs to estimate the increment in C, below stall, ДО, produced by a flap deflection. Not only is this needed in connection with the

wing lift, but A Ci is required also in analyzing the effectiveness of movable control surfaces, which frequently resemble plain flaps.

If an airfoil section has a lift curve slope of Cla and lowering its flap produces an increment of Д Ci, the angle of zero lift, a0i, is decreased by

(3.47)

The rate of decrease of a0/ per unit increase in the flap angle Sf is referred to as the flap effectiveness factor, r. Thus, for a flapped airfoil, the lift coefficient can be written as

Ct – C(„(a + rSf)

where/ a is the angle of attack of the airfoil’s zero lift line with the flap undeflected.

Theoretically т is a constant for a given flap geometry but, unfortunately, flap behavior with Sf is rather nonlinear and hence т must be empirically corrected by a factor 17 to account for the effects of viscosity. Including 17, Equation 3.48 becomes,

Ci = Ci„(a + T17 Sf)

The functions t and 17 can be obtained from Figures 3.32 and 3.33. Figure 3.33 is empirical and is based on data from References 3.15, 3.17, 3.19, and 3.20. Although there is some scatter in the data, as faired, the comparisons between the various types of flaps are consistent. The double-slotted flap delays separation on the upper surface, so that the decrease in flap effective­ness occurs at higher flap angles than for the other flap types. The same can be said of the slotted flap relative to the plain and split flaps. The plain flap is fairly good out to about 20° and then apparently the flow separates from the upper surface and the effectiveness drops rapidly, approaching the curve for split flaps at the higher flap angles. In A sense the flow is always separated on the upper surface of a split flap. Thus, even for small flap angles, the effective angular movement of the mean camber line at the trailing edge of an airfoil with a split flap would only be about half of the flap displacement.

In the case of the double-slotted flap it should be emphasized that this curve in Figure 3.33 is for an optimum flap geometry. The trailing segment of the flap is referred to as the main flap and the leading segment is called the vane. In applying Equation 3.49 and Figures 3.32 and^>.33 to the double – slotted flap, the total flap chord should be used together’with the flap angle of the main flap. Usually, the deflection angle of the vane’is less than that for the main flap for maximum lift performance.

Figure 3.32 is based on the thin airfoil theory^represented by Equation 3.39. As an exercise, derive the expression for т given on the figure, r can also be obtained using the numerical methods that led to Figures 3.17 and

3.18. As another exercise, apply Weissinger’s approximation to the flapped airfoil using only two point vortices to represent the airfoil. Placing one vortex on the quarter chord of the flap and the other on the quarter chord of the remainder of the airfoil leads to

3(3-2 Oc, 4(l-c/)c/ + 3

where Cf is the fraction of chord that is flapped. Equation 3.50 is ap­proximately 10% lower than Figure 3.32 for cflc values of around 0.25.

The angle of attack at which the flapped airfoil stalls is generally less than that for the plain airfoil. Hence, the increment in because of the flap is not as great as the increment in Q at an angle below the stall. Denoting these increments by ДС^ and ДС/, respectively, it is obvious that the ratio ДС^/ДС, must depend on cflc. If cflc, for example, is equal to 1.0, in a sense the entire airfoil is the flap and Дmust be zero. Systematic data on ДС^/ДС/ are sparse. Figure 3.34 has been drawn based on a limited number of data points and should be used with discretion.

As an example, in using Figures 3.32, 3.33, and 3.34, consider the prediction of Clni„ for a 23012 airfoil equipped with a 30% chord split flap deflected 60° and operating at a Reynold’s number of 3.5 x Ю6. From Figure 3.32, t = 0.66 for Cflc = 0.3 and from Figure 3.33, tj = 0.35 for a split flap deflected 60°. Hence from Equation 3.49, ДQ is equal to

Д C, = Qtij S

= (0.105)(0.66)(0.35)(60) (3.51)

= 1.46

In Equation 3.51, C(a of 0.105 is obtained from Reference 3.1. Using Figure 3.34, the ratio of ДC/max to Д Ct is obtained as 0.66. Hence,

ДС/_ = 0.96

According to Figure 3.27, C/max for a plain 23012 airfoil equals 1.65 at R = 3.5 x 106. Thus, for the flapped airfoil, C|max is predicted to be 1.65 + 0.96, or 2.61. This result compares closely with Figure 3.26a. If the procedure is repeated for other flap angles, close agreement is also obtained with the figure. However for a flap chord ratio of 0.1, the predicted values of C(max based on Figures 3.32 to 3.34 are higher than those shown in Figure 3.26a.